The cell cycle is the sequence of events whereby a cell grows, replicates its DNA and divides. During balanced growth there must be some coordination between the synthesis of new cell components--enzymes, structural proteins, membranes, ribosomes, DNA--and the division of a cell: in some average sense, each component must double during the cell cycle and then be fairly divided between the two daughter cells. It is commonly assumed that this coordination is achieved by a molecular mechanism that senses overall increase in cell size and triggers cell division when a target size is reached, provided of course that DNA is fully replicated. The specific aim of this proposal is to investigate the hypothesis of size-control of cell division by deriving statistical properties of model mechanisms and comparing these theoretical properties with experimental observations of asynchronous, proliferating cell cultures. As bits and pieces of the division-control mechanism are discovered by modern molecular and genetic techniques, the experience gained by the proposed theoretical approach will be valuable in putting together a complete picture of the regulatory system for cell growth and division. Since cell growth and division are fundamental processes in several areas of medical science (e.g., tumor growth, developmental disorders, and the spread of pathogenic microorganisms), basic research on the underlying regulatory mechanisms is vital to the interests of national health.